Question

In APQR, ray PS is the bisector of QPR, Q
Q-S-R. If QS = 4.8 cm, SR = 3.6 cm, find
4.8 cm PQ: PR.

Answer 1

Given,

$In \: \triangle \: PQR△PQR \: ray \: PSPS \\ is \: the \: bisector \: of \angle QPR$

And QS=4.8, SR=3.6

If a ray bisects an angle of a triangle, then its divides the opposite side of the triangle into segments that are proportional to the other two sides.

From figure of triangle,

$∴ \frac{PQ}{QS}=\frac{PR}{SR}$

$⇒\frac{PQ}{4.8}=\frac{PR}{3.6}$

$⇒\frac{PQ}{PR}=\frac{4.8}{3.6}$

$⇒\frac{PQ}{PR}=\frac{4}{3}$

∴ PQ:PR=4:3

So, The value ofPQ:PR is 4:3